Should they be merged?
They definitely have overlap. encounters is a more general tag, and covers things that encounter-design doesn't; the design tag meanwhile focuses directly on issues around building/designing/etc. encounters, making it more usefully focused for some questions' purposes than the general tag.
Is this ideal? Eh, it's not lovely. I have personally been brought up short trying to figure out the tagging with these two, since it's not always obvious. But they do have distinct domains even though they have overlap, so they're appropriate subjects for tagging. The ecounter-design tag is the more frequently used one by a factor of 3 (design has ~150 questions; the general tag has ~50), which is what justifies its existence as a specialisation of the more general tag. The more general tag continues to justify its existence by just covering things that the design tag doesn't.
Ideal no, but “perfect is the enemy of good enough.” These tags do their jobs well enough.
As always though, tags tend to get misapplied or just not updated when a newer tag is made (encounters is newer than the design tag) — where this has happened with these two tags it's useful to retag old questions to use the tags more consistently.
I think they're different and are sometmies being used differently. Encounter-design questions are mostly all about designing encounters. Encounter questions are frequently about post-encounter questions - though a couple prominent questions tagged encounters should be encounter-design (the diplomacy one and the plot device one just on the top page of results). Some of the rest aren't about questions being asked in advance about how to design an encounter, however, they are being asked by players or afterwards. But there's a lot that perhaps should be encounter-design instead.
- retag the outliers, and leave the questions that encounter-design isn't appropriate for (they skipped a fight do they get xp... when can I draw my sword in an encounter...
- merge encounters with encounter-design and figure out what to do with the outliers
- merge them into encounters and not worry about it
I think #3 is probably the best choice in terms of work for the value. This way [encounters] is mostly about encounter design, but also about the fringe of other related questions too.